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%I #26 Oct 13 2022 02:49:38
%S 1,2,5,12,28,66,156,368,868,2048,4832,11400,26896,63456,149712,353216,
%T 833344,1966112,4638656,10944000,25820224,60917760,143723520,
%U 339087488,800010496,1887468032,4453111040,10506243072,24787422208,58481066496,137974619136
%N Number of n-length words on {0,1,2} in which 0 appears only in runs of length 2.
%C Apparently a(n) = A239333(n).
%H Colin Barker, <a href="/A255115/b255115.txt">Table of n, a(n) for n = 0..1000</a>
%H D. Birmajer, J. B. Gil, and M. D. Weiner, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Gil/gil6.html">On the Enumeration of Restricted Words over a Finite Alphabet</a>, J. Int. Seq. 19 (2016) # 16.1.3, example 10.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,2).
%F a(n+3) = 2*a(n+2) + 2*a(n) with n>1, a(0) = 1, a(1) = 2, a(2)=5.
%F G.f.: -(x^2+1) / (2*x^3+2*x-1). - _Colin Barker_, Feb 15 2015
%F a(n) = A052912(n)+A052912(n-2). - _R. J. Mathar_, Jun 18 2015
%t RecurrenceTable[{a[0] == 1, a[1] == 2, a[2]== 5, a[n] == 2 a[n - 1] + 2 a[n - 3]}, a[n], {n, 0, 29}]
%o (PARI) Vec(-(x^2+1)/(2*x^3+2*x-1) + O(x^100)) \\ _Colin Barker_, Feb 15 2015
%Y Cf. A000930, A239333, A239340, A254657, A254600, A254664.
%K nonn,easy
%O 0,2
%A _Milan Janjic_, Feb 14 2015
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